Rory's Mini Cooper was in the parking lot next to the duck pond, but when he and Amy got into it, it had moved in front of the book store, where previously there was no car.
When the TARDIS is lying on its side in Amy's garden, its doors are open outward. The TARDIS doors always open inward.
During The Doctor's rooftop conversation with the Atraxi, Rory can be seen standing behind him holding a selection of jackets and ties. As the Atraxi are reviewing the various incarnations of The Doctor, one of the jackets (a dark reddish brown jacket) can be seen on the ground to Rory's left. When The Doctor says the line "Hello, I'm The Doctor", the coat is still on the ground, but the scene immediately cuts to a closeup with Rory still holding the jacket in his arms.
After eating the fish custard, the kitchen clock shows just after 9:30 pm as The Doctor and Amy head upstairs to examine the 'crack'. They're in the bedroom for about 5 minutes, then The Doctor leaves, Amy comes back, packs her bag, and goes back outside. The clock at that time shows 11:30 pm, before we see time elapsing as she waits. The total time elapsed between these two shots cannot possibly be 2 hours.
When The Doctor remembers what he saw when everyone except Rory were photographing the sun, the black car is already parked in front of the red one, but we only see it arrive in the next scene. Also The Doctor and Amy are not in in that shaky camera sequence even though their known location is visible.
The Doctor is standing next to the door when Amy hits him with the cricket bat but he falls to the floor on his right shoulder. He should have hit the door and either landed face down or on his left side afterwards.
When The Doctor flicks through the photos on Rory's phone, he flicks one way, the photos go the other. Some regard that as a goof, but on some phones (like Nokia 5230) that is how they're normally browsed.
The exterior of Amelia's house doesn't match the interior - When they are standing outside her room there are stairs going up & down but only 2 storeys from the outside.
But some attics have stairs leading to them.
But some attics have stairs leading to them.
When young Amelia Pond gives The Doctor the apple, he takes it with his left hand, and although we never see him put it in his pocket we can assume he puts it in his left trouser pocket. Later when older Amy traps The Doctor by locking his necktie in a car door, The Doctor pulls the same apple out of his right pocket. However, there is always the possibility that The Doctor moved the apple between pockets in the time between leaving young Amelia in 1996 and meeting her older self in 2008.
When The Doctor asks how many rooms there are Amy says 5 & the Doctor says 6 but there isn't enough room for 6 doors - by the stairs going down there are 3 doors (including Prisoner Zero's room) & by the stairs going up there is Amy's room and the room opposite. There is nowhere for the entrance to a sixth room because the stairs are in the way.
As 'young' Amy is taking her suitcase downstairs to wait for The Doctor, daylight can be seen under the door of the "missing" room, even though it's night time.
On the close-up of Rory's Royal Leadworth Hospital identification badge, the issue date is shown as issued on 30 November 1990, when the character would have been younger than 10 years old. (When asked about this in New York by an American fan on 13 April 2010 and whether it was part of the time-travel plot, Executive Producer/Showrunner Steven Moffat commented that "I have never actually looked at Rory's name tag to be completely honest with you... it's not a significant plot thing" and that it was simply a production error.)
In the very opening scene, the Earth is shown rotating in the wrong direction (turning westward). If this happened, the sun would rise in the west, which would be more astonishing than the sky "going wibbly."
On the hospital roof, when The Doctor asks the Atraxi, "Is this world protected?" they show various short clips of aliens from the show's history, but some of these, such as the Ood and the Hath, never threatened Earth, so there would be no reason for the Atraxi to have video footage of them from scanning and monitoring the planet.
The Doctor didn't recognise Amy as being the grown-up Amelia, but in Love & Monsters (2006) he recognised the adult Elton as the child he'd met before.